A couple years ago I noticed a neighbor's yard that had a ton of dandelions. He didn't treat or do anything. By mid-summer, his lawn looked like everyone else's lawn. In short, dandelions die out all by themselves, no action required.

Now, if you want lush grass, thick enough to choke out dandelions and most weeds before they even start, that's a different story. That takes work.

Ugh, weeds, the eternal battle. I’ve been pulling creeping Charlie for years to get our lawn in better shape and now dandelions are tearing their ugly heads. My husband who has a PhD in organic chemistry is a chemophobe but this time I’m opting for chemicals. I also have soil and lots of grass seed at the ready to fill in bald spots when done! You may enjoy this piece by Bob Vila, good luck! https://bobvila.com/articles/how-to-get-rid-of-dandelions/

You could hire a lawn care company to apply chemicals to try to resolve the issue. My husband and I have had pretty good luck with minimizing dandelions with these IFA fertilizer / weed control series.

https://ifacountrystores.com/2017/lawncare/beautiful-lawn-four-easy-steps/

I also regularly walk around the lawn with a bucket and a dandelion digger and dig up every single dandelion I can find. But it would be tough to do with the number you have now. It's important to get the dandelions up before they seed and make sure to dig up the root.

On the bright side, a dandelion-filled lawn is great for birds. Our goldfinches have minor interest in birdfeeders but get pretty excited when the "lawn" goes to seed.

Dandelions are perennial weeds. They don't just 'die off' by themselves! In fact, if left in place, they will simply get larger and more robust with a deeper tap root that is even harder to remove.

With an infestation that pervasive, it might be best to just clean everything out and start over. Unless you lay sod or hydroseed, the window for starting a new lawn won't happen until late summer or early fall so you have plenty of time to address the weeds. Any broadleaf lawn weed herbicide will address dandelions, so you can start there. Unfortunately, other than hand digging/manual removal, there is no "natural' way of removal.

We used to have lots of dandelions ... we just dig them when we see them, and every year there are fewer. This year I could probably count them on my fingers. If the tap root breaks, it'll be back, but maybe less vigorous. First, those white seed heads need to be carefully plucked and disposed of in the trash, where they cannot do any harm. Then you get a weeder tool and dig them out ... same routine next year, except you'll be faster and get to them before they go to seed, and repeat.

We do it the easy way. We hired a lawn service that routinely sprays. We didn't have one for the past summer. Our original lawn service sold the company and the new ones weren't any good. Not having that service for one summer our lawn has dandelions all over this spring and getting bald spots again. We just hired a new service.